avarage value?

Question

h(x) = 3-x , 0<=x<2
x/2 , 2<=x<=4

average value h(x) on [0,4] is ???

i am right if i do like this?
i integrate both equation then sum them up after i divide the amount by 4?

Answer 1

The average value of a function is calculated by the formula

1/(b - a) * Integral (a to b, h(x) dx )

In our case, a = 0 and b = 2, and h(x) = 3 - x, so we have

1/(2 - 0) * Integral (0 to 2, (3 - x) dx )
(1/2) * [ 3x - (1/2)x^2 ] {evaluated from 0 to 2}
(1/2) * { [ 3(2) - (1/2)(2)^2] - [ 3(0) - (1/2)(0)^2 ] }
(1/2) * { [ 6 - 2] - [0 - 0] }
(1/2) [-4]
-2

Try the second equation.

Answer 2

That will give you an approximate average.

You should integrate from 0 to 4 for h(x), then divide by the integral of 1 from 0 to 4.

Answer 3

Sounds good to me!